arXiv:2412.04121cs.LGcs.AI2024-12

用深度学习加速瞬态有限元分析,同时预测节点与单元解。

DeepFEA: Deep Learning for Prediction of Transient Finite Element Analysis Solutions

  • 用ConvLSTM分支双卷积网络并行预测节点和单元解
  • 2D/3D场景下误差低于3%,推理速度提升100倍
  • 适合需快速高精度模拟的工程与生物医学场景

有限元分析(FEA)是模拟物理现象的强大工具,但计算成本高昂。近年来机器学习发展出代理模型以加速FEA,但仍难以同时实现对节点与单元的瞬态解预测,并适用于二维与三维域。为此,本文提出DeepFEA,一种基于深度学习的框架,采用多层卷积长短期记忆网络(ConvLSTM)分支为两个并行卷积神经网络,分别预测节点与单元解。该网络通过新型自适应学习算法——节点-单元损失优化(NELO)进行优化,最小化两分支的误差,从而实现瞬态FEA解的预测。在结构力学领域的三个公开数据集上进行实验评估,结果表明DeepFEA在2D与3D仿真场景中均实现低于3%的归一化均值与均方根误差,推理时间比传统FEA快两个数量级。相比之下,现有先进方法在多维输出与动态输入预测上仍面临挑战。此外,其鲁棒性在真实生物医学场景中得到验证,证实其适用于准确高效的FEA模拟预测。

原文摘要 · Abstract (English)

Finite Element Analysis (FEA) is a powerful but computationally intensive method for simulating physical phenomena. Recent advancements in machine learning have led to surrogate models capable of accelerating FEA. Yet there are still limitations in developing surrogates of transient FEA models that can simultaneously predict the solutions for both nodes and elements with applicability on both the 2D and 3D domains. Motivated by this research gap, this study proposes DeepFEA, a deep learning-based framework that leverages a multilayer Convolutional Long Short-Term Memory (ConvLSTM) network branching into two parallel convolutional neural networks to predict the solutions for both nodes and elements of FEA models. The proposed network is optimized using a novel adaptive learning algorithm, called Node-Element Loss Optimization (NELO). NELO minimizes the error occurring at both branches of the network enabling the prediction of solutions for transient FEA simulations. The experimental evaluation of DeepFEA is performed on three datasets in the context of structural mechanics, generated to serve as publicly available reference datasets. The results show that DeepFEA can achieve less than 3% normalized mean and root mean squared error for 2D and 3D simulation scenarios, and inference times that are two orders of magnitude faster than FEA. In contrast, relevant state-of-the-art methods face challenges with multi-dimensional output and dynamic input prediction. Furthermore, DeepFEA's robustness was demonstrated in a real-life biomedical scenario, confirming its suitability for accurate and efficient predictions of FEA simulations.

有限元分析深度学习瞬态模拟加速计算

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